Symmetry analysis for a fourth-order noise-reduction partial differential equation

  title={Symmetry analysis for a fourth-order noise-reduction partial differential equation},
  author={P. G. L. Leach and Andronikos Paliathanasis},
  journal={Quaestiones Mathematicae},
  pages={1541 - 1552}
Abstract We apply the theory of Lie symmetries in order to study a fourth-order 1+2 evolutionary partial differential equation which has been proposed for the image processing noise reduction. In particular we determine the Lie point symmetries for the specific 1+2 partial differential equations and we apply the invariant functions to determine similarity solutions. For the static solutions we observe that the reduced fourth-order ordinary differential equations are reduced to second-order… 
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